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The Semi Simple Zeta Function Of Shimura Varieties Associated To Quaternion Algebras
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Book Synopsis The semi-simple zeta function of quaternionic Shimura varieties by : Harry Reimann
Download or read book The semi-simple zeta function of quaternionic Shimura varieties written by Harry Reimann and published by Springer. This book was released on 2006-11-14 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is concerned with the Shimura variety attached to a quaternion algebra over a totally real number field. For any place of good (or moderately bad) reduction, the corresponding (semi-simple) local zeta function is expressed in terms of (semi-simple) local L-functions attached to automorphic representations. In an appendix a conjecture of Langlands and Rapoport on the reduction of a Shimura variety in a very general case is restated in a slightly stronger form. The reader is expected to be familiar with the basic concepts of algebraic geometry, algebraic number theory and the theory of automorphic representation.
Book Synopsis The Semi-simple Zeta Function of Shimura Varieties Associated to Quaternion Algebras by : Harry Reimann
Download or read book The Semi-simple Zeta Function of Shimura Varieties Associated to Quaternion Algebras written by Harry Reimann and published by . This book was released on 1995 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Zeta Functions of Simple Algebras by : Roger Godement
Download or read book Zeta Functions of Simple Algebras written by Roger Godement and published by Springer. This book was released on 2006-11-14 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis p-Adic Automorphic Forms on Shimura Varieties by : Haruzo Hida
Download or read book p-Adic Automorphic Forms on Shimura Varieties written by Haruzo Hida and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early years of the 1980s, while I was visiting the Institute for Ad vanced Study (lAS) at Princeton as a postdoctoral member, I got a fascinating view, studying congruence modulo a prime among elliptic modular forms, that an automorphic L-function of a given algebraic group G should have a canon ical p-adic counterpart of several variables. I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p-adic automorphic forms, allocating 10 to 15 years from that point, putting off the intended arithmetic study of Shimura varieties via L-functions and Eisenstein series (for which I visited lAS). Although it took more than 15 years, we now know (at least conjecturally) the exact number of variables for a given G, and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general (nonholomorphic) cohomological automorphic forms on automorphic manifolds (in a markedly different way). When I was asked to give a series of lectures in the Automorphic Semester in the year 2000 at the Emile Borel Center (Centre Emile Borel) at the Poincare Institute in Paris, I chose to give an exposition of the theory of p-adic (ordinary) families of such automorphic forms p-adic analytically de pending on their weights, and this book is the outgrowth of the lectures given there.
Book Synopsis On the Zeta Function of Quaternionic Shimura Varieties by : Harry Reimann
Download or read book On the Zeta Function of Quaternionic Shimura Varieties written by Harry Reimann and published by . This book was released on 1998 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Université de Montréal. Centre de recherches mathématiques Publisher :Publications CRM ISBN 13 : Total Pages :520 pages Book Rating :4.3/5 (91 download)
Book Synopsis The Zeta Functions of Picard Modular Surfaces by : Université de Montréal. Centre de recherches mathématiques
Download or read book The Zeta Functions of Picard Modular Surfaces written by Université de Montréal. Centre de recherches mathématiques and published by Publications CRM. This book was released on 1992 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although they are central objects in the theory of diophantine equations, the zeta-functions of Hasse-Weil are not well understood. One large class of varieties whose zeta-functions are perhaps within reach are those attached to discrete groups, generically called Shimura varieties. The techniques involved are difficult: representation theory and harmonic analysis; the trace formula and endoscopy; intersection cohomology and $L2$-cohomology; and abelian varieties with complex multiplication.The simplest Shimura varieties for which all attendant problems occur are those attached to unitary groups in three variables over imaginary quadratic fields, referred to in this volume as Picard modular surfaces. The contributors have provided a coherent and thorough account of necessary ideas and techniques, many of which are novel and not previously published.
Book Synopsis Zeta Functions of Simple Algebras by : Roger Godement
Download or read book Zeta Functions of Simple Algebras written by Roger Godement and published by . This book was released on 2014-01-15 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Zeta Functions of Simple Algebras by : Roger Godement
Download or read book Zeta Functions of Simple Algebras written by Roger Godement and published by . This book was released on 1972 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Clay Mathematics Institute. Summer School Publisher :American Mathematical Soc. ISBN 13 :9780821838440 Total Pages :708 pages Book Rating :4.8/5 (384 download)
Book Synopsis Harmonic Analysis, the Trace Formula, and Shimura Varieties by : Clay Mathematics Institute. Summer School
Download or read book Harmonic Analysis, the Trace Formula, and Shimura Varieties written by Clay Mathematics Institute. Summer School and published by American Mathematical Soc.. This book was released on 2005 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.
Book Synopsis Automorphic Forms, Representations and $L$-Functions by : Armand Borel
Download or read book Automorphic Forms, Representations and $L$-Functions written by Armand Borel and published by American Mathematical Soc.. This book was released on 1979-06-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 1052 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modular Forms by : Toshitsune Miyake
Download or read book Modular Forms written by Toshitsune Miyake and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of the earlier book written by Koji Doi and the author, who revised it substantially for this English edition. It offers the basic knowledge of elliptic modular forms necessary to understand recent developments in number theory. It also treats the unit groups of quaternion algebras, rarely dealt with in books; and in the last chapter, Eisenstein series with parameter are discussed following the recent work of Shimura.
Book Synopsis Reviews in Number Theory, 1984-96 by :
Download or read book Reviews in Number Theory, 1984-96 written by and published by American Mathematical Society(RI). This book was released on 1997 with total page 1084 pages. Available in PDF, EPUB and Kindle. Book excerpt: These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews (MR) between 1984 and 1996. This is the third such set of volumes in number theory: the first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.
Book Synopsis Automorphic Forms and Shimura Varieties of PGSp (2) by : Yuval Z. Flicker
Download or read book Automorphic Forms and Shimura Varieties of PGSp (2) written by Yuval Z. Flicker and published by World Scientific. This book was released on 2005 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called OC liftings.OCO This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2, ?) in SL(4, ?). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to LanglandsOCO program in the area of automorphic representations. It includes a proof of known cases of ArtinOCOs conjecture."
Book Synopsis Formes Automorphes (I): Questions about slopes of modular forms by : Centre Émile Borel
Download or read book Formes Automorphes (I): Questions about slopes of modular forms written by Centre Émile Borel and published by . This book was released on 2005 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first of a series of two devoted to automorphic forms from a geometric and arithmetic point of view. They also deal with certain parts of the Langlands program. The themes treated in this volume include $p$-adic modular forms, the local Langlands correspondence for $GL(n)$, the cohomology of Shimura varieties, their reduction modulo $p$, and their stratification by Newton polygons. The book is suitable for graduate students and research mathematicians interested in number theory, algebra, and algebraic geometry.
Book Synopsis Automorphic Forms, Shimura Varieties, and L-functions by : Laurent Clozel
Download or read book Automorphic Forms, Shimura Varieties, and L-functions written by Laurent Clozel and published by . This book was released on 1990 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno
Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.
